# Re: st: STATA: multivariate probit w/ bootstrap

 From "Stas Kolenikov" To statalist@hsphsun2.harvard.edu Subject Re: st: STATA: multivariate probit w/ bootstrap Date Thu, 1 May 2008 12:11:46 -0500

```Then you should extend the code I gave, with either -post- or
-bootstrap: mymvprobit-, and include WTP estimation for each sample,
to be -posted- or -bootstrap-ped along with the coefficients. If you
can express WTP as the function of estimated parameters, then you
should consider -nlcom- that would give you the delta method standard
errors -- if you can technically do that, I would not bother with the
bootstrap. You would probably find yourself wasting a week of your
time setting your bootstrap up properly, to find the standard errors
only differ in the third decimal point from those in -nlcom-.

If you want to do something really cool, you should set this up as a
Bayesian estimation procedure, where you would repeatedly sample
unobserved epsilons for your probit part, and parameter values from
(approximation to) the posterior. Then for each constellation of the
parameter estimates, you can compute the WTP, and get an MCMC
distribution of these. That's some work for WinBUGS, or may be R,
rather than Stata, though.

On 5/1/08, Daniel R. Petrolia <Petrolia@agecon.msstate.edu> wrote:
> Stas,
>   Thanks a lot for your detailed suggestions.  We are interested in willingness-to-pay (WTP) estimates, the mean of which requires both the estimated coefficients and the variable means to calculate.  What we would like to get is a confidence interval on our mean WTP, which, based on research, it is suggested that one bootstrap to derive a sample of anywhere from 50 to 1000 mean WTP estimates, and drop 2.5% of obs in the tails for a 95% C.I.  Well, to do this, we need to estimate our model over a number of bootstrapped samples.  This is easy enough with probit or even biprobit, but in our case, we have 3 probit equations whose errors are correlated and thus, ideally, should be estimated together.  Thus, the need for mvprobit or triprobit.
>   Our latest attempt is to generate the required number of samples using SAS, then estimated the regression on each sample manually.

--
Stas Kolenikov, also found at http://stas.kolenikov.name